Theorem mulcomi 8175

Description: Commutative law for multiplication. (Contributed by NM, 23-Nov-1994.)

Hypotheses

Ref	Expression
axi.1	|- A e. CC
axi.2	|- B e. CC

Assertion

Ref	Expression
mulcomi	|- ( A x. B ) = ( B x. A )

Proof of Theorem mulcomi

Step	Hyp	Ref	Expression
1		axi.1	. 2 |- A e. CC
2		axi.2	. 2 |- B e. CC
3		mulcom 8151	. 2 |- ( ( A e. CC /\ B e. CC ) -> ( A x. B ) = ( B x. A ) )
4	1, 2, 3	mp2an 426	1 |- ( A x. B ) = ( B x. A )

Syntax hints:   = wceq 1395   e. wcel 2200  (class class class)co 6013   CCcc 8020   x. cmul 8027

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 108  ax-mulcom 8123

This theorem is referenced by:  mulcomli  8176  8th4div3  9353  numma2c  9646  nummul2c  9650  9t11e99  9730  binom2i  10900  fac3  10984  tanval2ap  12264  pockthi  12921  decsplit1  12991  decsplit  12992  sincosq4sgn  15543  2logb9irrALT  15688  2lgsoddprmlem2  15825  2lgsoddprmlem3d  15829